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Kinetic facilitated models and the Mode Coupling Theory (MCT) model B are within those systems known to exhibit a discontinuous dynamical transition with a two step relaxation. We consider a general scaling approach, within mean field…
We study the yielding transition of a two dimensional amorphous system under shear by using a mesoscopic elasto-plastic model. The model combines a full (tensorial) description of the elastic interactions in the system, and the possibility…
The dynamic surface critical behavior of macroscopic systems whose dynamic bulk critical behavior is described by model $B$ is investigated. The semi-infinite extensions of bulk model $B$ introduced in a previous treatment [Phys. Rev. B 49,…
The critical behavior at the ordinary transition in semi-infinite n-component anisotropic cubic models is investigated by applying the field theoretic approach in d=3 dimensions up to the two-loop approximation. Numerical estimates of the…
Conformal field theories with central charge $c\le1$ on random surfaces have been extensively studied in the past. Here, this discussion is extended from their equilibrium distribution to their critical dynamics. This is motivated by the…
We study the conditions under which the critical behavior of the three-dimensional $mn$-vector model does not belong to the spherically symmetrical universality class. In the calculations we rely on the field-theoretical renormalization…
The model of landscape erosion, introduced in [{\it Phys. Rev. Lett.} {\bf 80}: 4349 (1998); {\it J. Stat. Phys.} {\bf 93}: 477 (1998)] and modified in [{\it Theor. Math. Phys.} - in press; arXiv:1602.00432], is advected by anisotropic…
Phenomenological scaling arguments suggest the existence of universal amplitudes in the finite-size scaling of certain correlation lengths in strongly anisotropic or dynamical phase transitions. For equilibrium systems, provided that…
We show by a detailed study of the mean-field approximation, the Gaussian approximation, the perturbation expansion, and the field-theoretic renormalization-group analysis of a $\varphi^{3}$ theory that its instability fixed points with…
We develop a global bifurcation theory for two classes of nonlinear elastic materials. It is supposed that they are subjected to anti-plane shear deformation and occupy an infinite cylinder in the reference configuration. Curves of…
We propose a variational framework for accretive surface growth driven by an optimality principle. Rather than prescribing a kinetic law, the configuration at each time step is obtained, within a time-discrete setting, as the solution of a…
Key traits of unicellular species, like cell size, often follow scale-free or self-similar distributions, hinting at the possibility of an underlying critical process. However, linking such empirical scaling laws to the critical regime of…
We present results of numerical studies of the two dimensional XY model with four and eight fold symmetry breaking fields. This model has recently been shown to describe hydrogen induced reconstruction on the W(100) surface. Based on…
Astronomical observations suggest that the Universe may be anisotropic on the largest scales. In order to model this situation, we develop a new approach to cosmology that allows for large-scale anisotropy to emerge from the growth of…
Recent advances in conformal field theory and critical phenomena have focused on the characterization of boundary or defects in a conformally invariant system. In this Letter we study the critical behavior of the three-dimensional Ising…
New field theoretic renormalization group methods are developed to describe in a unified fashion the critical exponents of an m-fold Lifshitz point at the two-loop order in the anisotropic (m not equal to d) and isotropic (m=d close to 8)…
A field theoretic renormalization group method is presented which is capable of dealing with crossover problems associated with a change in the upper critical dimension. The method leads to flow functions for the parameters and coupling…
A novel class of integrable surfaces is recorded. This class of O surfaces is shown to include and generalize classical surfaces such as isothermic, constant mean curvature, minimal, `linear' Weingarten, Guichard and Petot surfaces and…
We study the universal critical behaviour near weakly first-order phase transitions for a three-dimensional model of two coupled scalar fields -- the cubic anisotropy model. Renormalization-group techniques are employed within the formalism…
We construct a family of stochastic growth models in 2+1 dimensions, that belong to the anisotropic KPZ class. Appropriate projections of these models yield 1+1 dimensional growth models in the KPZ class and random tiling models. We show…